In two separate experiments equal quantities of alkyl halide, `C_4H_9Cl`, were treated at the same temperature with equal volume of 0.1 molar and 0.2 molar solutions of NaOH respectively. In the two experiments, `t_(1//2)` of the two reaction were the same. The most likely structure of halide is

Options

A. `CH_3CH_2CH_2CH_2Cl`
B. `CH_3CH(Cl)CH_2CH_3`
C. `(CH_3)_2CHCH_2Cl`
D. `(CH_3)_3C Cl`

Explanation

To solve the problem, we need to analyze the information given about the reactions of the alkyl halide \( C_4H_9Cl \) with sodium hydroxide (NaOH) in two separate experiments.

### Step 1: Understand the Reaction Conditions
We have two experiments where equal quantities of \( C_4H_9Cl \) are treated with two different concentrations of NaOH (0.1 M and 0.2 M). Both reactions are conducted at the same temperature and with equal volumes of the NaOH solution.

**Hint:** Pay attention to how concentration affects reaction rates in different types of nucleophilic substitution reactions (SN1 vs. SN2).

### Step 2: Analyze the Half-Life (t1/2)
The problem states that the half-life (\( t_{1/2} \)) of the reactions in both experiments is the same. In nucleophilic substitution reactions, the half-life can provide insight into the mechanism of the reaction:

- For **SN1 reactions**, the half-life is independent of the concentration of the nucleophile.
- For **SN2 reactions**, the half-life is dependent on the concentration of both the substrate and the nucleophile.

**Hint:** Since the half-lives are the same despite different concentrations of NaOH, this suggests that the reaction follows an SN1 mechanism.

### Step 3: Determine the Structure of the Alkyl Halide
SN1 reactions are favored by tertiary (3°) alkyl halides because they can form stable carbocations. The order of stability for carbocations is:
- Tertiary (3°) > Secondary (2°) > Primary (1°)

Since the reaction is likely SN1, we can conclude that the structure of \( C_4H_9Cl \) is most likely a tertiary alkyl halide.

**Hint:** Look for the option that represents a tertiary alkyl halide among the choices provided.

### Step 4: Identify the Correct Structure
Among the possible structures for \( C_4H_9Cl \), the one that is a tertiary alkyl halide is the most likely candidate.

**Hint:** Check the given options for a structure that has the chlorine atom attached to a carbon that is connected to three other carbons.

### Conclusion
Based on the analysis, the most likely structure of the halide \( C_4H_9Cl \) is a tertiary alkyl halide.

### Final Answer
The most likely structure of the halide is a tertiary alkyl halide.